This paper derives the optimal debt ratio and dividend payment strategies for an insurance company. Taking into account the impact of reinsurance policies and claims from the credit derivatives, the surplus process is stochastic that is jointly determined by the reinsurance strategies, debt levels, and unanticipated shocks. The objective is to maximize the total expected discounted utility of d...

The classical and relativistic Hamilton-Jacobi approach is applied to the one-dimensional homogeneous potential, V (q) = αqn, where α and n are continuously varying parameters. In the non-relativistic case, the exact analytical solution is determined in terms of α, n and the total energy E. It is also shown that the non-linear equation of motion can be linearized by constructing a hypergeometri...

We consider the problem of determining in a dynamical way the optimal capacity level of an investment project that operates within a random economic environment. In particular, we consider an investment project that yields a payoff at a rate that depends on its installed capacity level and on a random economic indicator such as, for instance, the price of the project’s output commodity. We mode...

Classical chaos is often characterized as exponential divergence of nearby trajectories. In many interesting cases these trajectories can be identified with geodesic curves. We define here the entropy by S = ln χ(x) with χ(x) being the distance between two nearby geodesics. We derive an equation for the entropy, which by transformation to a Riccati-type equation becomes similar to the Jacobi eq...

The spectral properties of Jacobi and periodic Jacobi matrices are analyzed and algorithms for the construction of Jacobi and periodic Jacobi matrices with prescribed spectra are presented. Numerical evidence demonstrates that these algorithms are of practical utility. These algorithms have been used in studies of the periodic Toda lattice, and might also be used in studies of inverse eigenvalu...

This paper addresses the optimal scheduling of the liquidation of a portfolio using a new angle. Instead of focusing only on the scheduling aspect like Almgren and Chriss in [2], or only on the liquidity-consuming orders like Obizhaeva and Wang in [31], we link the optimal trade-schedule to the price of the limit orders that have to be sent to the limit order book to optimally liquidate a portf...

We present some new results, together with a number of particularly simple and userfriendly versions of results obtained in recent years by the author and M. Malisoff, on the uniqueness of solutions of the Hamilton-Jacobi-Bellman equation (HJBE) for deterministic finite-dimensional optimal control problems under non-standard hypotheses. Our approach is completely controltheoretic and totally se...

We propose a continuous-time model of trading among risk-neutral agents with heterogeneous beliefs. Agents face quadratic costs-of-carry on their positions and as a consequence, their marginal valuation of the asset decreases when the magnitude of their position increases, as it would be the case for risk-averse agents. In the equilibrium models of investors with heterogeneous beliefs that foll...